Method for operating a plant of hydrocarbons containing organo-sulfur compounds by means of a thermo-cinetic model and a compositional tank simulation

ABSTRACT

A method for determining an amount of hydrogen sulfide produced by a phenomenon of aquathermolysis induced by a thermal process, such as steam injection. 
     On the basis of a compositional representation of the hydrocarbons, an elementary reaction scheme is defined that is representative of a material balance for the element sulfur, as well as a system of reactions representative of the aquathermolysis reaction. Then a kinetic model is constructed taking into account the reaction scheme, the system of reactions, atomic balances relating to each of the reactions and relating at least to the sulfur, carbon and hydrogen atoms. Then a thermodynamic model is constructed and the resultant thermokinetic model is calibrated on the basis of experimental measurements. Finally, an amount of hydrogen sulfide is determined by performing a compositional reservoir simulation taking into account the resultant calibrated thermokinetic model. 
     Application notably to the exploration and exploitation of oil deposits, for example.

The invention relates to the field of oil exploration, and more particularly the field of exploitation of a deposit of hydrocarbons containing organosulfur compounds, by a thermal process such as a steam injection process.

During the exploitation of reservoirs of heavy crudes by a steam injection process, a phenomenon of aquathermolysis occurs, which may generate hydrogen sulfide (H₂S). In fact, this type of reservoir may often have high sulfur contents. The thermal processes make it possible, by supplying calories and raising the temperature, to reduce the viscosity of the heavy crudes and thus make them producible.

Aquathermolysis is defined in the present description as a set of physicochemical reactions between rock impregnated with crude oil (or with bitumen) and steam, at temperatures between 200° C. and 300° C.

Hydrogen sulfide is a gas that is both extremely corrosive and highly toxic, or even lethal above a certain concentration. Thus, predicting the concentration of H₂S in the gas produced during recovery assisted by steam injection helps, on the one hand, to reduce the costs of production by adapting the completion materials and the gas treatment devices, optimizing the operating conditions, and on the other hand to avoid emissions that are dangerous to people and the environment.

One technical problem is prediction of the amount of H₂S generated in relation to the nature of the crude, the reservoir conditions and the conditions of steam injection. If we wish to predict the risk of production of H₂S based on a reservoir model (used by flow simulators), a kinetic model of hydrogen sulfide generation is required.

Moreover, the physicochemical reactions associated with the phenomenon of aquathermolysis produce a change in the composition of heavy oil. It may therefore be advantageous if the kinetic model used for predicting hydrogen sulfide generation could also predict the variations in the composition of the oil in the reservoir. This capacity would in fact make it possible to predict the effects of the steam injection process on the quality of the oil produced.

PRIOR ART

The following documents will be cited in the description:

Barroux, C., Lamoureux-Var, V., Flauraud, E., 2013. Forecasting of H₂S Production due to Aquathermolysis Reactions, Paper SPE 164317, presented at the SPE Middle East Oil and Gas Show and Conference, Manam, Bahrain.

Belgrave J. D. M., Moore R. G., Ursenbach R. G, (1997), “Comprehensive kinetic models for the aquathermolysis of heavy oils”, Journal of Canadian Petroleum Technology, v 36, n 4, p 38-44.

Boduszynski, M. M. 1987. Composition of Heavy Petroleums. 1. Molecular Weight, Hydrogen Deficiency, and Heteroatom Concentration as a Function of Atmospheric Equivalent Boiling Point up to 1400° F. (760° C.). Energy & Fuels, 1, 2-11.

Coats, K. H. 1980. In-Situ Combustion Model. SPE Journal, December, 533-554.

Merdrignac, I. and Espinat D. 2007. Physicochemical Characterization of Petroleum Fractions: the State of the Art. Oil & Gas Science and Technology—Rev. IFP, 62, 1, 7-32.

Crookston, R. B., Culham, W. E., Chen, W. H. 1979. A Numerical Simulation Model Recovery Processes for Thermal Recovery Processes. SPE 6724, SPE J., February, 37-58.

Fan T. and Buckley, J., Rapid and Accurate SARA Analysis of Medium Gravity Crude Oils, Energy Fuels, 2002, 16 (6), pp 1571-1575.

Lamoureux-Var, V. and Lorant, F. (2005a). Barroux, C., (2013), Using Geochemistry to Address H₂S Artificial Formation as a Result of Production Risk due to Steam Injection for EOR: a Compositional Kinetic Approach. In Oil Sands. Paper 13HOCC-P-412-SPE 97810, SPE/PS-CIM/CHOA International Thermal Operations and Heavy Oil Symposium, 1-3 November Conference, Calgary, Alberta, Canada, 11-14 June.

Lamoureux-Var, V. and Lorant, F. (2005b). Experimental evaluation of H₂S yields in reservoir rocks submitted to steam injection. Paper D08, 13th European Symposium on Improved Oil Recovery, EAGE, Budapest, Hungary, 25-27 April.

Peng, D. Y., and Robinson, D. B. 1976. A New Two-Constant Equation of State. Industrial and Engineering Chemistry Fundamentals, 15, 59-64.

Søreide, I. and Whitson, C. H. 1992. Peng-Robinson Predictions for Hydrocarbons CO₂, N₂, and H₂S with Pure Water and NaCl Brine. Fluid Phase Equilibria, 77, 217-240.

A method is known from patent application FR 2892817 (U.S. Ser. No. 11/588,365) for constructing a kinetic model for estimating the mass of hydrogen sulfide produced by aquathermolysis of a rock containing crude oil. This method uses a mass-based compositional representation of the crude oil by classes of chemical compounds of the SARA type (description of hydrocarbons in four mass fractions or pseudo-constituents: Saturates, Aromatics, Resins and Asphaltenes; see for example (Fan and Buckley, 2002)) and describes the variation of the distribution of sulfur in said mass fractions of the oil and a so-called insoluble fraction (which represents the solid receiving a part of the sulfur initially held in the oil during the aquathermolysis reactions). The method proposed is based on an elementary reaction scheme for the element sulfur, obtained by mass balances for the element sulfur distributed in the various fractions (SARA and solid). However, this scheme cannot be used in a reservoir simulation. In fact, reservoir simulation requires information on pseudo-constituents, each described by a molecule, and not only by a mass as in patent application FR 2892817 (U.S. Ser. No. 11/588,365).

Application FR 3002969 (U.S. Ser. No. 14/200,682) is also known, which aims to transform the kinetic model based on the distribution of sulfur of application FR 2892817 (U.S. Ser. No. 11/588,365) into a molecular compositional kinetic model. This model was developed with the aim of predicting the production of H₂S resulting from the aquathermolysis reactions in the context of reservoir simulation. However, this model has a number of drawbacks. Firstly, the atomic balance for sulfur, assumed to be respected by this method (since the compositional kinetic model is constructed around the reaction scheme for the element sulfur developed in application FR 2892817 (U.S. Ser. No. 11/588,365)), is not so in practice. In fact, application of this method shows that the stoichiometric coefficients derived on the basis of the reaction scheme for sulfur are unable to reproduce the results observed in the laboratory, notably the variations in mass of the SARA fractions and H₂S over time. The stoichiometric coefficients must therefore be modified in order to match the observations in aquathermolysis experiments. The atomic balance for sulfur, which after all forms the basis of this compositional kinetic model, is then no longer respected once the kinetic model is calibrated. Moreover, the kinetic model developed in this application, based solely on the element sulfur, cannot respect the average atomic balances of the atomic elements, other than sulfur, making up the pseudo-molecules representing the various SARA fractions, namely carbon (C), hydrogen (H) and oxygen (O). These limitations have the result that the reaction scheme described in application FR 3002969 (U.S. Ser. No. 14/200,682) does not allow experimental data to be incorporated, such as the results of elemental analyses performed in the laboratory, which might, however, act as constraints to be respected by linking the number of atoms of the constituent elements of each of the pseudo-constituents to its number of carbon atoms. Moreover, the kinetic model of application FR 3002969 (U.S. Ser. No. 14/200,682) does not allow the element oxygen to be taken into account, which prevents prediction of the evolution of water (H₂O) and carbon dioxide (CO₂) during the aquathermolysis reactions. However, H₂O is an essential reactant of the aquathermolysis reactions, without which the reactions cannot take place. The possibility of taking water into account in the compositional reaction scheme of the aquathermolysis model therefore seems to be important when enhanced accuracy of the results of reservoir simulation is desired, and in order to reinforce the predictive aspect of the model. Finally, the mass balance between reactants and products of each of the reactions on which application FR 3002969 (U.S. Ser. No. 14/200,682) is based is indeed respected during calibration of the model, but this constraint is only satisfied by adjusting the stoichiometric coefficients of the saturates fraction. In fact, the method described in patent application FR 3002969 (U.S. Ser. No. 14/200,682), which is based on the reaction scheme for sulfur in patent FR 2892817 (U.S. Ser. No. 11/588,365), deduces the stoichiometric coefficient associated with the saturates by effecting a simple mass balance between reactants and products for each reaction. Now, as water is not incorporated in the compositional reaction scheme, like numerous chemical species, a simple mass balance for the reactions of the model cannot allow a stoichiometric coefficient suitable for the saturates to be determined. Therefore, within the model in application FR 3002969 (U.S. Ser. No. 14/200,682), the saturates perform the role of adjustment variable in order to respect the mass balance of each of the reactions of the aquathermolysis reaction scheme.

The invention relates to a method for exploiting a hydrocarbon deposit containing organosulfur compounds by means of a thermokinetic model and a compositional reservoir simulation. The kinetic model constructed by the method according to the invention adheres more closely to the theory of the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances), but can also take into account certain experimental measurements that are available (such as elemental analyses), and thus contribute to more accurate quantification of the hydrogen sulfide emissions.

The Method According to the Invention

Thus, the present invention relates to a method for exploiting an underground deposit of hydrocarbons containing organosulfur compounds. The method according to the invention comprises the following steps:

-   -   A. determining an amount of hydrogen sulfide (H₂S) produced over         time by a phenomenon of aquathermolysis induced by a thermal         process such as steam injection into said deposit, based on a         grid representation of said deposit, from experimental         measurements carried out on at least one sample of said         hydrocarbons and/or a rock sample from said deposit, employing         the following steps:         -   i. constructing an elementary reaction scheme representative             of a material balance for the element sulfur based on at             least one compositional representation of the hydrocarbons,             said representation describing said hydrocarbons as various             pseudo-constituents, at least one solid pseudo-constituent,             at least one constituent H₂S, and pseudo-stoichiometric             coefficients relating to said pseudo-constituents and             constituents;         -   ii, constructing a kinetic model based on at least one             system of reactions simulating said phenomenon of             aquathermolysis, said reaction scheme, atomic balances             relating to each of said reactions of said system of             reactions, said balances relating at least to the sulfur,             carbon and hydrogen atoms, and said system of reactions             being a function of stoichiometric coefficients at least             relating to said pseudo-constituents and constituents;         -   iii. constructing a thermodynamic model of the             pseudo-constituents of said compositional representation;         -   iv. calibrating a thermokinetic model, consisting of said             kinetic model and said thermodynamic model, on the basis of             said experimental measurements;         -   v. determining said amount of hydrogen sulfide (H₂S)             produced by performing a compositional reservoir simulation,             by means of a compositional and reactive thermal simulator,             said simulator employing said thermokinetic model, and by             means of said grid representation;     -   B. determining the conditions of exploitation of said deposit as         a function of said amount of hydrogen sulfide;     -   C. producing said hydrocarbons by applying said conditions of         exploitation.

Advantageously, said compositional representation of the hydrocarbons may consist of the following pseudo-constituents: saturated hydrocarbons, aromatic hydrocarbons, resins and asphaltenes.

Preferably, said experimental measurements may consist of aquathermolysis experiments simulated in the laboratory.

According to one embodiment of the invention, step ii) may be carried out according to the following steps:

-   -   a) defining a system of reactions describing said phenomenon of         aquathermolysis in said deposit, said system being a function of         at least said pseudo-constituents and at least the constituents         H₂S and H₂O, and of said stoichiometric coefficients relating to         each of said pseudo-constituents and constituents;     -   b) defining a first system of equations establishing, for each         of said reactions, atomic balances for the atomic elements H, C,         S and O;     -   c) defining a second system of equations linking said         pseudo-stoichiometric coefficients of said reaction scheme to         said stoichiometric coefficients of said system of reactions,         the sum of said pseudo-stoichiometric coefficients of said         reaction scheme being equal to 1;     -   d) determining an expression for said stoichiometric         coefficients of said system of reactions by jointly solving said         systems of equations.

Preferably, a third system of equations may be defined, linking the number of sulfur, carbon and oxygen atoms as a function of the number of carbon atoms for each of said pseudo-constituents and constituents.

Advantageously, said number of sulfur, carbon and oxygen atoms may be linked as a function of said number of carbon atoms for each of said pseudo-constituents via ratios determined by elemental analyses carried out on products of aquathermolysis simulated in the laboratory.

The method as claimed in one of the preceding claims, in which, in step iii), at least kinetic parameters of said thermokinetic model are calibrated.

The method as claimed in one of claims 1 to 6, in which, in step iii), kinetic parameters of said thermokinetic model and said pseudo-stoichiometric coefficients of said reaction scheme are calibrated.

According to one embodiment of the invention, variation over time of the amount of each of said pseudo-constituents of said compositional representation may additionally be determined in step A).

According to one embodiment of the invention, said conditions of exploitation may be determined by adapting completion materials and/or gas treatment devices as a function of said amount of hydrogen sulfide.

According to one embodiment of the invention, said conditions of exploitation may consist of modifying steam injection conditions so as to minimize said amount of hydrogen sulfide.

According to one embodiment of the invention, said conditions of exploitation may be determined so as to keep production of hydrogen sulfide below a legal maximum content.

The invention further relates to a computer program product downloadable from a communication network and/or recorded on a computer-readable medium and/or executable by a processor, comprising program code instructions for implementing the method according to the above description, when said program is executed on a computer.

BRIEF DESCRIPTION OF THE FIGURES

Other features and advantages of the method according to the invention will become clear on reading the following description of nonlimiting embodiment examples, referring to the appended figures that are described below.

FIG. 1 shows the evolution over time of the mass of H₂S relative to the initial total mass of the SARA pseudo-constituents, obtained by carrying out the present invention and by the experimental method.

FIGS. 2A, 2B, 2C and 2D show the evolution over time of the mass of the pseudo-constituents SAT, ARO, RES and ASP respectively, relative to their initial mass, obtained by carrying out the present invention and by the experimental method.

FIG. 3 shows the simulated production of H₂S as a function of time obtained by carrying out the present invention and by measurements in situ.

FIGS. 4A and 4B show the evolution of the molar fraction of the pseudo-constituents ASP, ARO, RES, SAT and of the constituent H₂S over time, obtained by carrying out the present invention.

DETAILED DESCRIPTION OF THE METHOD ACCORDING TO THE INVENTION

The following definitions are used in the description of the invention:

-   -   hydrocarbons: used in the broad sense, as is often the case in         reservoir engineering, this means both hydrocarbons in the         strict sense, made up of hydrogen and carbon atoms exclusively         (the Saturates fraction in the case of the SARA compositional         representation), and other organic compounds additionally         comprising heteroelements such as oxygen and sulfur         (sulfur-containing Aromatics, Resins, and Asphaltenes fractions         in the case of the SARA compositional representation).     -   constituent: means a molecular species such as hydrogen sulfide         (H₂S), methane (CH₄), water (H₂O);     -   pseudo-constituent: means a mixture of molecular species that         may be likened to a single molecular species for the present         problem;     -   atomic element: means an atomic elementary species such as         sulfur S, carbon C, hydrogen H, etc.;     -   reaction scheme for sulfur: means an elementary kinetic model         constructed on the basis of the distribution of elemental sulfur         among the constituent H₂S, the pseudo-constituents of a         compositional representation of the hydrocarbons (such as the         SARA representation) and a solid pseudo-constituent. This         reaction scheme for sulfur makes it possible to describe the         generation of H₂S as a function of the sulfur contained in the         pseudo-constituents of a compositional representation of the         hydrocarbons, when the reservoir rock is brought into contact         with water at a temperature between 150° C. and 340° C., as a         function of the temperature and duration of contact between the         reservoir rock and the water. This scheme aims to represent the         manner in which the element sulfur is distributed during         cracking of the organosulfur compounds contained in the         hydrocarbons in the broad sense, generated by the         aquathermolysis reaction. Note that an elementary reaction         scheme for the element sulfur is not usable as it is in a         reservoir simulation, which uses information on         constituents/pseudo-constituents of the molecular type, and not         information on atomic elements.     -   stoichiometric coefficients: these are coefficients indicating         the molecular proportions of the various species involved in the         equilibrium of a chemical reaction.     -   pseudo-stoichiometric coefficients: these are coefficients         indicating the proportions by mass of the various species         involved in a chemical reaction. Pseudo-stoichiometric         coefficients are used in the case of pseudo-constituents whose         molecular weight is unknown or poorly known, and for which the         chemical equations are therefore written in proportions by mass.

The present invention relates to a method, and the use thereof, for modeling the production of hydrogen sulfide (H₂S) induced by reactions taking place in an underground deposit of hydrocarbons when said deposit is submitted to a thermal recovery process, in particular to a steam injection process, the reactions then being due to a phenomenon of aquathermolysis.

The method according to the invention comprises at least the following steps:

1. Determination of an amount of hydrogen sulfide (H₂S) produced

-   -   1.1. Construction of a reaction scheme for sulfur     -   1.2. Construction of a kinetic model     -   1.3. Construction of a thermodynamic model     -   1.4. Calibration of the thermokinetic model     -   1.5. Execution of reservoir simulation         2. Determination of the conditions of exploitation as a function         of the amount of hydrogen sulfide         3. Production of the hydrocarbons

The following are required for carrying out the present invention:

-   -   experimental measurements performed on at least one sample of         petroleum or rock from the deposit under investigation:     -   Firstly, experimental measurements are necessary for carrying         out the step of calibration of the thermokinetic model of the         method according to the invention. For this purpose,         aquathermolysis experiments are carried out in the laboratory,         consisting of heating a rock sample from the deposit or         petroleum with water, at a constant temperature and under a         controlled pressure for a specified time. To calibrate the         kinetic parameters (frequency factors, activation energies) of         the thermokinetic model and, if necessary (i.e. if these         coefficients are not already known), the pseudo-stoichiometric         coefficients of the reaction scheme for sulfur, several         aquathermolysis experiments may be repeated, at different         temperatures and for different times. Then, at the end of these         aquathermolysis experiments, the mass of the various         constituents/pseudo-constituents involved in the aquathermolysis         reactions, and their content of atomic sulfur by weight, are         measured. From this it is possible to deduce a first mass         balance for all the constituents/pseudo-constituents; it is the         sum of the masses of the constituents/pseudo-constituents after         reaction divided by the sum of the masses of the         constituents/pseudo-constituents put in the system prior to         reaction. From this it is then possible to deduce a second mass         balance for the distribution of atomic sulfur by mass for all         the constituents/pseudo-constituents; it is the sum, for all the         constituents/pseudo-constituents, of the ratios between the mass         of atomic sulfur in a constituent/pseudo-constituent and the         mass of total sulfur involved in the system. We may deduce, from         these two calculations of mass balance, on the one hand the         evolution of the proportion by mass of the         constituents/pseudo-constituents over time and for different         temperatures, and on the other hand the evolution of the         distribution of atomic sulfur by mass among the         constituents/pseudo-constituents over time and for different         temperatures. These repeated experiments make it possible to         calibrate the kinetic parameters of the thermokinetic model, but         also the pseudo-stoichiometric coefficients of the reaction         scheme for sulfur.     -   Secondly, experimental measurements may be useful as constraints         for constructing the kinetic model of the method according to         the invention, or else for reducing the number of unknowns of         this kinetic model. An elemental analysis of the products of         aquathermolysis experiments carried out in the laboratory may be         performed for this purpose. Well known by geochemistry         specialists, elemental analysis of a pseudo-constituent consists         of quantifying its proportion by mass of atomic elements such as         carbon, hydrogen, sulfur, etc. These measurements give access to         the ratios between elementary atomic species S/C, H/C and O/C         for these pseudo-constituents.     -   a compositional and reactive thermal reservoir simulator: a         reservoir simulator is a digital program, executed on a         computer, which is used for predicting the flow of fluids (oil,         brine and gas) through the porous medium of the reservoir, as         well as the production of these fluids at the surface by means         of a well. In the case of a thermal simulator, the temperature         in the reservoir is not constant but varies for example as a         function of heat conduction in the reservoir or phase changes of         the various constituents if the simulation is also         compositional. In fact, in the context of a compositional         simulation, the hydrocarbon phases (gas and oil) are defined as         a set of constituents or pseudo-constituents. The properties of         these phases (density, viscosity, etc.) are then calculated as a         function of their composition. Finally, a compositional         simulator is described as reactive if it contains a module of         chemical reactions that allows the         constituents/pseudo-constituents defined to react chemically         with one another. An example of such software is the PUMAFLOW         software (IFP Energies nouvelles, France).     -   a grid representation of the deposit under investigation: also         called “reservoir model” or “geomodel”, it is a kind of model of         the subsoil constructed with the aim of describing, as precisely         as possible, the structure, the petrophysical properties, the         properties of the fluids, etc., of the deposit under         investigation. This model is generally represented on a         computer, and consists of a mesh or grid, each of the cells of         this grid having one or more values of petrophysical properties         (porosity, permeability, saturation etc.). A reservoir model         must verify, as far as possible, all of the data collected for         the terrain: logging data measured along the wells, measurements         carried out on rock samples taken from the wells, data deduced         from seismic acquisition campaigns, production data such as the         flow rates of oil and water, the pressure variations etc. A         specialist in reservoir simulation has full knowledge of methods         for constructing this grid representation of a deposit.

The main steps of the present invention are detailed below.

1. Determination of an Amount of Hydrogen Sulfide (H₂S) Produced

The objective of this step is to estimate, by compositional reservoir simulation, the amount of hydrogen sulfide (H₂S) that would be produced if a thermal process were used for exploiting an underground reservoir impregnated with oil or bitumen containing organosulfur compounds (i.e. impregnated with hydrocarbons in the broad sense).

1.1. Construction of a Reaction Scheme for Sulfur

In this step, an elementary reaction scheme is constructed that is representative of a material balance for the element sulfur, also called a reaction scheme for sulfur. The reaction scheme for sulfur according to the invention requires definition of a compositional representation of the hydrocarbons.

According to a preferred embodiment of the present invention, as in patent application FR 2892817 (U.S. Ser. No. 11/588,365), a compositional representation by classes of chemical compounds of the SARA type, described for example in (Fan and Buckley, 2002), is used. This representation, used conventionally in industry, consists of describing the hydrocarbons in four fractions: saturated hydrocarbons (Saturates), aromatic hydrocarbons (Aromatics), Resins and Asphaltenes, and supplying the mass fraction of each of these fractions. More precisely, the SARA representation consists of:

-   -   a pseudo-constituent representing the class of compounds not         containing sulfur; this pseudo-constituent is assigned to the         class of Saturates, and is denoted by SAT,     -   at least one pseudo-constituent representing the class of         Aromatics; this pseudo-constituent is denoted by ARO,     -   one or more pseudo-constituent(s) representing the class of         Resins; these pseudo-components are denoted by RES₁, RES₂, . . .         , RES_(p),     -   one or more pseudo-constituent(s) representing the Asphaltene         class; these pseudo-components are denoted by ASP₁, ASP₂, . . .         , ASP_(q).         These pseudo-constituents make it possible to simulate the fluid         phases, or phases that may become fluid, notably under the         effect of temperature, as in the case of steam injection.         Moreover, each of the sulfur-containing pseudo-constituents         {ARO, SLD₁, SLD₂, SLD_(s), RES₁, RES₂, . . . , RES_(p), ASP₁,         ASP₂, . . . , ASP_(q)} may be likened to a pseudo-molecule of         general formula R_(nR)S_(ns), where S denotes the sulfur atom of         mass Ms and R an ensemble of atoms regarded as a single         pseudo-atomic element of mass M_(R), n_(S), n_(R) denoting         respectively the numbers of S atoms and of pseudo-elements R in         the pseudo-molecule of molecular weight MW.

Moreover, the reaction scheme for sulfur according to the invention also takes into account at least:

-   -   one or more pseudo-constituents of the solid type, such as coke,         denoted by SLD₁, SLD₂, . . . , SLD_(s), these solid         pseudo-constituents numbering Ns. The pseudo-constituent of the         solid type is considered to represent the solid receiving a part         of the sulfur held back in the hydrocarbons during the         aquathermolysis reactions. This solid pseudo-constituent is a         product of the aquathermolysis reactions and describes the         pyrobitumen generated by these reactions.     -   a constituent H₂S.

Moreover, the reaction scheme for sulfur according to the invention is a function of pseudo-stoichiometric coefficients relating to the pseudo-constituents and constituents involved in said reaction scheme.

According to a preferred embodiment of the present invention, we use the elementary reaction scheme representative of a material balance for the element sulfur employed in patent application FR2892817, which describes the distribution of all the sulfur in the various pseudo-constituents mentioned above on the basis of the following assumptions:

-   -   it is thought that the saturates fraction does not contain         sulfur;     -   it is thought that the sulfur contained in the resins fraction         gives rise to hydrogen sulfide and is partly incorporated in the         solids and aromatics fractions;     -   it is thought that the sulfur contained in the asphaltenes         fraction gives rise to hydrogen sulfide and is partly         incorporated in the solids and aromatics fractions;     -   it is assumed, moreover, that the sulfur in the asphaltenes and         the sulfur in the resins do not interact;     -   furthermore, it is considered that several reactions coexist in         parallel within each fraction, these reactions being         characterized by different time constants.         Thus, according to this embodiment, cracking of the         sulfur-containing organic components present in the resins and         asphaltenes classes is assumed to be the main contribution to         the production of H₂S. In other words, the pseudo-constituents         of the asphalthenes and resins classes perform the role of         reactants in the elementary reaction scheme for sulfur according         to this embodiment.

According to a preferred embodiment of the invention, the elementary reaction scheme representative of a material balance for the element sulfur described in patent application FR 289281 is used, only considering two pseudo-constituents representing the resins class (designated RES1 and RES2), two pseudo-constituents representing the asphaltenes class (designated ASP1 and ASP2), and a single solid pseudo-constituent (designated SLD). Moreover, for each class of reactants (RESi and ASPi, with i=1, 2), it is assumed that the two associated pseudo-constituents each generate a reaction with its own reaction kinetics. This leads to the construction of a reaction scheme for sulfur with four reactions as described by a system of reactions of the form:

S ^(RES1) →a _(S1H2S) S ^(H2S) +a _(S1ARO) S ^(ARO) +a _(S1SLD) S ^(SLD)

S ^(RES2) →a _(S2H2S) S ^(H2S) +a _(S2ARO) S ^(ARO) +a _(S2SLD) S ^(SLD)

S ^(ASP1) →a _(S3H2S) S ^(H2S) +a _(S3ARO) S ^(ARO) +a _(S3SLD) S ^(SLD)

S ^(ASP1) →a _(S4H2S) S ^(H2S) +a _(S4ARO) S ^(ARO) +a _(S4SLD) S ^(SLD)

where S^(H2S), S^(RES1) and S^(RES2), S^(ASP1) and S^(ASP2), S^(ARO), S^(SLD), denote respectively the sulfur retained by the H₂S, by the pseudo-constituents RES1 and RES2 representing the resins class, by the pseudo-constituents ASP1 and ASP2 representing the asphaltenes class, by the pseudo-constituent ARO representing the aromatics class, and by the pseudo-constituent SLD of the solid type, the coefficients a_(SrConstk) (with 1≤r≤4 and Const_(1≤k≤3=){H2S, ARO, SLD}) being pseudo-stoichiometric coefficients defined in such a way that the reactions defined above are balanced with respect to mass. According to one embodiment of the present invention, the coefficients a_(SrConstk) (with 1<r≤4 and 1<k S 3) are estimated by taking mass balances for the distribution of sulfur using the Geokin Compo software (IFPEN, Energies nouvelles).

1.2 Construction of a Kinetic Model

In this step, a kinetic model is constructed for estimating the evolution of the mass of hydrogen sulfide produced by a phenomenon of aquathermolysis. According to one embodiment of the invention, the kinetic model may in addition be used for estimating the evolution over time of the composition of the hydrocarbons of the deposit under investigation, i.e. the variation over time of the amount of each of the pseudo-constituents of the compositional representation selected in the preceding step 1.1.

The kinetic model according to the invention is defined on the basis of at least one system of reactions simulating the phenomenon of aquathermolysis, the elementary reaction scheme representative of a material balance for the element sulfur as defined in step 1.1, atomic balances relating to each of the reactions of the system of reactions thus defined, the balances relating at least to the sulfur, carbon and hydrogen atoms. Moreover, according to the invention, the system of reactions simulating said phenomenon of aquathermolysis is a function of stoichiometric coefficients relating at least to the pseudo-constituents defined in step 1.1 and at least to the constituent H₂S.

The kinetic model according to the invention may be obtained by the nonlimiting sequence of the following steps:

-   -   1.2.1. Definition of a system of reactions simulating         aquathermolysis     -   1.2.2. Definition of atomic balances for each of the reactions     -   1.2.3. Establishment of a link between the pseudo-stoichiometric         coefficients of the reaction scheme and the stoichiometric         coefficients of the system of reactions     -   1.2.4. Determination of the stoichiometric coefficients of the         system of reactions         Steps 1.2.1 to 1.2.4 of this preferred embodiment are detailed         below.

1.2.1. Definition of a System of Reactions Simulating Aquathermolysis

In this substep, it is a matter of defining a system of reactions describing said phenomenon of aquathermolysis in said deposit. According to the invention, the system of reactions simulating aquathermolysis is a function of at least the pseudo-constituents defined in step 1.1 and at least the constituent H₂S. Moreover, this system of reactions is expressed as a function of stoichiometric coefficients relating to each of the pseudo-constituents and constituents involved in the reactions.

According to a preferred embodiment of the present invention, each of the pseudo-constituents defined in step 1.1 is represented by a pseudo-molecule of the type C_(nC)H_(nH)S_(nS)O_(nO), where nC, nH, nS, and nO are respectively the number of atoms of carbon, hydrogen, sulfur and oxygen in said pseudo-molecule. By taking oxygen into account in the kinetic model it is notably possible to incorporate water (H₂O) and carbon dioxide (CO₂) in the system of reactions simulating aquathermolysis. In particular, by taking water into account in the kinetic model it is possible to improve the accuracy of the prediction of the mass balances, but also ensure that the aquathermolysis reactions are only simulated when water molecules are indeed present. Moreover, the pseudo-molecules allow the appropriate average thermodynamic characteristics of the pseudo-constituents of the compositional representation selected and or of the solid pseudo-constituents to be incorporated in the kinetic model. In order to determine the pseudo-molecule associated with each pseudo-constituent, it is assumed that the elemental analysis of each pseudo-constituent is constant throughout the aquathermolysis reactions. This leads to a system of reactions (designated (2) hereinafter) of the form:

RES1+a _(1H20) H ₂ O→a _(1SAT) SAT+a _(1ARO) ARO+a _(1H2S) H ₂ S+a _(1SLD) SLD+a _(1CO2) C0₂  (r1)

RES2+a _(2H20) H ₂ O→a _(2SAT) SAT+a _(2ARO) ARO+a _(2H2S) H ₂ S+a _(2SLD) SLD+a _(2CO2) C0₂  (r2)

ASP1+a _(3H20) H ₂ O→a _(3SAT) SAT+a _(3ARO) ARO+a _(3H2S) H ₂ S+a _(3SLD) SLD+a _(3CO2) C0₂  (r3)

ASP1+a _(4H20) H ₂ O→a _(4SAT) SAT+a _(4ARO) ARO+a _(4H2S) H ₂ S+a _(4SLD) SLD+a _(4CO2) C0₂  (r4)

SAT+a _(5H20) H ₂ O→a _(5CO2) C0₂ +a _(5CH4) CH ₄  (r5)

where a_(i Const j) are the stoichiometric coefficients associated with each pseudo-constituent/constituent Const_(j)={1:7}={H₂O, SAT, ARO, H₂S, SLD, CO₂, CH₄} involved in the system of reactions thus defined, with have a_(i Const j)≤0 for the reactants (to the left of the arrow in a reaction) and a_(i Const j)≥0 for the products (to the right of the arrow in a reaction) of this system of reactions. Note that the fifth reaction (designated r5) models cracking of the saturates in the presence of steam, which makes it possible (in contrast to patent application FR 3002969 (U.S. Ser. No. 14/200,682) that does not have a reaction involving the saturates) to take into account the variation of mass of the saturates class, said variation being observed during aquathermolysis experiments performed in the laboratory.

Moreover, each chemical reaction of the system of reactions according to the invention is characterized by its own reaction rate K_(i={1:5}) that depends on parameters called kinetic parameters. According to one embodiment of the present invention, each reaction rate is expressed by an Arrhenius law, familiar to a person skilled in the art, of the form: K_(i)=A_(i)e^(−Ei/RT), where A_(i) is the frequency factor, E_(i) is the activation energy, R is the ideal gas constant and T is the temperature of the system.

1.2.2. Definition of Atomic Balances for Each of the Reactions

In this substep, it is a matter of defining atomic balances at least for carbon (C), sulfur (S) and hydrogen (H) for each of the reactions of the system of reactions established in step 1.2.1.

According to a preferred embodiment of the present invention, an atomic balance for carbon (C), sulfur (S), hydrogen (H) and oxygen (O) is defined for each of the reactions of the system of reactions established in (2). We then arrive at a system of equations of the form:

n _(C) _(Reactant i) =Σ_(j=1) ^(j=N) a _(l Product j) n _(C) _(Product j)

n _(S) _(Reactant i) =Σ_(j=1) ^(j=N) a _(l Product j) n _(S) _(Product j)

n _(H) _(Reactant i) +2a _(i H20)=Σ_(j=1) ^(j=N) a _(l Product j) n _(H) _(Product j)

n _(O) _(Reactant i) +2a _(i H20)=Σ_(j=1) ^(j=N) a _(l Product j) n _(O) _(Product j)   (3)

with the index i corresponding to the number of reactions (from i=1 to i=5) of system (2) and Reactant_(i={1:5})={RES1, RES2, ASP1, ASP2, SAT}, index j corresponding to the products of the reaction and Product_(j={1:6})={SAT, ARO, H₂S, SLD, CO₂, CH₄}, and n_({C, S, H, O} {Reactant i, Product j}) corresponding respectively to the number of carbon, sulfur, hydrogen and oxygen atoms present in the constituent or pseudo-constituent considered.

According to a preferred embodiment of the present invention, and for the purpose of solving the systems of equations involved in the present invention, in addition the number of sulfur, hydrogen and oxygen atoms is expressed as a function of the number of carbon atoms for each of the pseudo-constituents and constituents considered in system of reactions (2). For this purpose, we may use the ratios S/C, H/C and O/C of the SARA pseudo-constituents and SLD (designated Rx/c with x={S,H,O}), which is information accessible from experimental measurements performed in the laboratory, notably by elemental analysis of the products of aquathermolysis simulated in the laboratory. Note that these ratios change slightly over time, but these changes can be neglected to a first approximation. Based on this assumption, a new set of equations can be written in the form:

n _(S) _(Component) ₁ =R _(S) _(/C) _(Component 1) n _(C) _(Component) ₁

n _(H) _(Component 1) =R _(H) _(/C) _(Component 1) n _(C) _(Component 1)

n _(O) _(Component 1) =R _(O) _(/C) _(Component 1) n _(C) _(Component 1) ,  (4)

with Component_(l={1:11})={RES1, RES2, ASP1, ASP2, ARO, SAT, SLD, H₂O, CO₂, H₂S, CH₄}, n_({S,H,O}Component 1) being the number of atoms of sulfur, hydrogen, and oxygen, respectively, in a pseudo-constituent/constituent Component_(l={1:11}), and n_(CComponent 1) being the number of carbon atoms in a pseudo-constituent/constituent Component_(l={1:11}). Note that the elementary ratios H/C and O/C of the constituents (H₂O, CO₂, H₂S, CH₄) involved in system of reactions (2) are immediate and do not have to be determined by elemental analysis.

1.2.3. Establishment of a Link Between the Pseudo-Stoichiometric Coefficients of the Reaction Scheme and the Stoichiometric Coefficients of the System of Reactions

In this substep, a link is established between the pseudo-stoichiometric coefficients of the reaction scheme for sulfur established in step 1.1 and the stoichiometric coefficients of the system of reactions simulating aquathermolysis established in step 1.2.1 This link can be expressed in the form of the following system of equations:

a _(i H2S) =a _(S) _(iH2S) n _(S) _(Reactant i)

a _(i ARO) =a _(S) _(1ARO) n _(S) _(Reactant i) /n _(S) _(ARO)

a _(i SLD) =a _(S) _(1SLD) n _(S) _(Reactant i) /n _(S) _(SLD)

a _(S) _(iH2S) +a _(S) _(iARO) +a _(S) _(iSLD) =1  (5)

1.2.4. Determination of the Stoichiometric Coefficients of the System of Reactions

In this step, it is a matter of determining an expression for the stoichiometric coefficients of system of reactions (2) by jointly solving the systems of equations (3), (4), and (5).

According to one embodiment of the present invention, it is possible to use a formal program, such as Maple (Maplesoft, Canada), in order to obtain an expression for the stoichiometric coefficients of system of reactions (2) as a function of the set of variables involved in the systems of equations (3), (4), and (5).

Thus, the kinetic model constructed by the method according to the invention allows better account to be taken of the theory of the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances for sulfur, but also for carbon, hydrogen and possibly oxygen, as well as the possibility of including water or carbon dioxide in the system of reactions), but also take into account certain experimental measurements available (such as elemental analyses).

By describing the pseudo-constituents by molecular formulas (of the pseudo-molecules), it is possible to deduce directly the thermodynamic properties that depend on these molecular formulas, notably by correlations based on the molecular weight. As the molecular description of the pseudo-constituents is also consistent with the system of reactions adopted for describing the aquathermolysis reactions, notably with its stoichiometric coefficients, a consistent set is obtained between the molecular pseudo-formulas of these pseudo-constituents, the system of reactions that describes aquathermolysis by causing these pseudo-constituents to interact, and finally the thermodynamic properties of these pseudo-constituents.

1.3 Construction of a Thermodynamic Model

In this step, it is a matter of constructing a thermodynamic model for estimating the properties or behavior of the liquid and/or vapor phases of mixtures of multiple constituents and pseudo-constituents, such as those encountered in situ in reservoirs of petroleum, bitumen or gas, or on the surface during exploitation of these same deposits, and offering the possibility of predicting the detailed composition of fluids produced during production, as a function of time.

In the reaction context of the invention, we need a compositional thermodynamic model where the compositions of nonaqueous and nonsolid phases are detailed using the same constituents and pseudo-constituents as those involved in construction of the reaction scheme for sulfur. According to one embodiment of the present invention, the molecular weight of each of the pseudo-constituents is selected as identical to that used for constructing the system of reactions, and the other thermodynamic parameters of each of the constituents are selected by correlation with their molecular weight, deduced in its turn from their pseudo-molecular formula. As for the solid or solids, they are characterized solely by their molecular weight and are not considered in the calculation of the properties of the oil, gas and water phases.

If we choose to use thermodynamics by correlation, the parameters of the constituents/pseudo-constituents in the correlations can be adjusted on the basis of calculations performed with an equation of state, where the parameters per constituent/pseudo-constituent are typically obtained from databases when it is a question of “pure substances”, such as H₂S, or when it is a question of pseudo-constituents, from correlations based at least partly on the molecular weight.

1.4 Calibration of the Thermokinetic Model

Thus, at the end of the preceding steps, we obtain a thermokinetic model, i.e. a model resulting from combining the kinetic model constructed in step 1.2 described above and the thermodynamic model constructed in step 1.3 described above. According to one embodiment of the present invention, the thermokinetic model according to the invention can be implemented in a reservoir simulator, with a view to calibration of the thermokinetic model.

In the present step, it is a matter of calibrating the previously constructed thermokinetic model, i.e. of adjusting the parameters of the thermokinetic model in question so that the results of numerical simulation of the phenomenon of aquathermolysis by the thermokinetic model are in agreement with the experimental measurements.

According to one embodiment of the present invention, the parameters to be adjusted are the pseudo-stoichiometric coefficients of the reaction scheme for sulfur (described in step 1.1) as well as the kinetic parameters (i.e. the frequency factors and the activation energies described in step 1.2) of the system of reactions of the kinetic model. Preferably, calibration of the thermokinetic model consists of adjustment of the kinetic parameters of the five reactions of the system of reactions defined by equation (2) and pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined by equation (1).

According to another embodiment of the invention, if the pseudo-stoichiometric coefficients of the reaction scheme for sulfur were determined beforehand on the basis of aquathermolysis experiments, calibration of the numerical results with the experimental measurements is obtained by adjusting only the kinetic parameters of the reactions, i.e. the frequency factors and the activation energies.

According to one embodiment of the present invention, calibration of the kinetic parameters of the five reactions of the system of reactions defined by system (2) and the pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined in equation (1) is carried out by means of an iterative inversion technique. More precisely, based on initial values for the parameters to be determined, an objective function is constructed, measuring the difference between the normed quantities predicted by systems (1) and (2) for H₂S and the pseudo-constituents of the compositional representation selected and their respective experimental measurements, then the values of these parameters are modified, iteration after iteration, until a minimum of the objective function is found. During calibration, reproduction of the normed experimental data for H₂S is preferred, as the quality of the predictions of H₂S production at the surface, in reservoir simulations involving aquathermolysis reactions, mainly depends on good prediction of this quantity. A great many algorithms for objective function minimization are known by a person skilled in the art, such as the Gauss-Newton method, the Newton-Raphson method or the conjugated gradient. According to a preferred embodiment of the present invention, the Gauss-Newton method is used as the algorithm for minimizing the objective function described above. An example of software using an inversion technique is the CougarFlow software (IFP Energies nouvelles, France), which can be coupled with the PumaFlow reservoir simulation software (IFP Energies nouvelles, France), in which the thermokinetic model defined above will have been implemented, for estimating the various terms of the objective function.

1.5 Application of the Simulation Reservoir

In this step, it is a matter of determining the amount of hydrogen sulfide (H₂S) produced over time by a phenomenon of aquathermolysis by performing a reservoir simulation, applied to the grid representation of the deposit under investigation, and by means of a compositional and reactive thermal simulator, said simulator using the previously defined and calibrated thermokinetic model.

Reservoir simulation involves performing calculations of phase equilibrium and calculations of phase properties, which will be detailed below.

1.5.1 Phase Equilibria

In compositional reservoir simulation with presence of steam as in the case under investigation, the phase equilibria between the “aqueous liquid” phase (called “water”), the “liquid hydrocarbon” phase (called oil), and the gas phase, are calculated using typically the following assumptions:

-   -   the gas phase may contain constituents such as H₂S, CO₂ and         steam, as well as pseudo-constituents of the compositional         representation of the hydrocarbons;     -   the oil phase contains all the pseudo-constituents of the         compositional representation of the hydrocarbons, may contain         H₂S and CO₂, but does not contain water;     -   the “water” phase is essentially more or less salty water, and         one option for dissolution of the         pseudo-constituents/constituents resulting from aquathermolysis         of the hydrocarbons in the aqueous phase can be activated for         example for H₂S which, like carbon dioxide (CO₂), may be         dissolved notably in an aqueous phase.

According to one embodiment of the invention, the equilibria between phases are calculated on the basis of equilibrium constants per constituent/pseudo-constituent calculated in the course of simulation (or precalculated before the simulation) from fugacities per constituent/pseudo-constituent per phase, obtained in their turn from an equation of state. Preferably, a cubic equation of state is used:

-   -   for distributing the constituents/pseudo-constituents between         oil and gas phases: in this case, one of the equations most         commonly used is the Peng-Robinson equation, described for         example in (Peng and Robinson, 1976);     -   for distributing the constituents/pseudo-constituents between         gas and water phases: in this case the equation most commonly         used is that of Søreide and Whitson, described for example in         (Søreide and Whitson, 1992).

Industrial reservoir simulation programs also offer the possibility of calculating the equilibria between phases starting from tabulated equilibrium constants, as a function of pressure and temperature and possibly as a function of a compositional index, which are introduced by the engineer as input data for the simulation.

Another possibility offered for gas-oil equilibria is for the equilibrium constants to be calculated from analytical correlations, the engineer then having to introduce the parameters of each constituent/pseudo-constituent into the correlations. These two possibilities, tabulated equilibrium constants or those obtained by analytical correlation, are the ones that are offered primarily by industrial software in a reaction and thermal context; a description of these options can be found in (Coats, 1980).

Since the inputs for calculating the equilibria are equilibrium constants per constituent, tabulated or by correlation, a methodology used by a person skilled in the art is to generate the tables or the parameters of the constituents/pseudo-constituents based on a reference equation of state. The tables must be generated for pressures and temperatures that may be encountered in the course of numerical reservoir simulation.

The parameters of the constituents/pseudo-constituents in the reference equation of state are typically the critical parameters (temperature, pressure, volume or compressibility factor), the acentric factor, and parameters of binary interactions between constituents/pseudo-constituents.

The thermodynamic parameters of pure substances such as H₂S are known and are listed by various organizations such as N.I.S.T. (National Institute of Standards and Technology, http://www.nist.gov). In contrast, the parameters of pseudo-constituents, critical parameters, acentric factor, and parameters of binary interactions must be estimated. A great many correlations are available, including correlations based on the molecular weight of the pseudo-constituent, its density and its boiling point, and these last two properties may in their turn be estimated by correlations based on the molecular weight of the pseudo-constituent. As a guide for choosing the correlations to use, it is possible to employ certain data relating to the nature of the pseudo-constituent (such as elemental analysis, which gives the mass distribution of different atomic elements), and/or its structure, taking inspiration for example from (Boduszynski, 1987).

Finally, it is should be added that the measured value of the molecular weight of heavy compounds is known to depend on the experimental technique used, for example as reported in (Merdrignac and Espinat, 2007).

Regardless of the degree of sophistication of the method used for determining them, the molecular weights of the heavy pseudo-constituents are still just estimates, which may be used as initial estimates in a process of optimization of parameters, notably of the number of carbon atoms of the pseudo-constituents, or not to be modified if they are considered to be sufficiently representative, or if it is found a posteriori that the values adopted a priori were a judicious choice.

1.5.2 Phase Properties

The phase properties for use in the calculations performed in numerical compositional reservoir simulation are, per phase: viscosity, enthalpy, molecular weight, molar density (inverse of molar volume), the product of these last two properties being equal to the density, estimation of which is indispensable for calculations of the gravitational effects, the latter in fact being linked to the differences in densities between phases. The molecular weights of the phases can be calculated directly from results of the calculations of equilibrium, which give the compositions of each phase.

Various possibilities are offered for calculating the molar volumes of the oil and gas phases:

-   -   using an equation of state, typically cubic, generally identical         to that used for the calculations of equilibrium, using the same         parameters per constituent as those used for calculating the         equilibria;     -   using correlations that are differentiated according to the         nature of the oil or gas phase, these correlations using         specific parameters defined per constituent.

For calculating the viscosities, it is possible to use a single correlation for the calculations of viscosity of the oil and gas phases or, more frequently for simulation of reservoirs of heavy oil, one correlation for the viscosity of the oil and a different correlation for the viscosity of the gas. These correlations use specific parameters defined per constituent/pseudo-constituent.

The enthalpies of the phases are usually calculated from specific heats defined per constituent/pseudo-constituent and per phase, and the specific heat per constituent/pseudo-constituent in the gas phase may alternatively be calculated from a specific heat per constituent/pseudo-constituent in the oil phase and a latent heat per constituent/pseudo-constituent. Further details may be found in Coats' work cited above, in the work of (Crookston, 1979), and in the reference manuals of industrial software for reservoir simulation such as PumaFlow.

The method according to the invention therefore makes it possible to model hydrocarbon-containing fluids in a mixture of constituents/pseudo-constituents, each of these constituents/pseudo-constituents being characterized by thermodynamic parameters for modeling the physical properties of the fluid, and moreover this thermodynamic modeling is consistent with a multi-reaction kinetic model, where one of the products of the reactions modeled is hydrogen sulfide (H₂S).

At the end of this step, through so-called “reservoir” simulation, we obtain the amounts of H₂S that may be generated during exploitation of oil deposits by steam injection, as well as the variations in the composition of the oil at the surface and in the reservoir, i.e. the variation over time of the amount of each of said pseudo-constituents of the compositional representation of the hydrocarbons selected in step 1.1.

2. Determination of the Conditions of Exploitation as a Function of the Amount of Hydrogen Sulfide

These amounts of hydrogen sulfide may be compared with an amount measured in the past (production history). We may then adjust parameters of the kinetic model and/or of the thermal model, so that the estimates are more accurate for the deposit under investigation. With these adjusted models it is possible to predict the production of H₂S from the deposit, for given exploitation conditions.

It is also possible to determine the conditions of exploitation on adapting the completion materials and/or the gas treatment devices, so as to limit the damage caused by acid attack.

It is also possible to modify the steam injection conditions in an attempt to reduce the amounts of H₂S produced.

It is also possible to compare the amount of hydrogen sulfide against a legal maximum content (from 10 to 50 ppm by volume, according to the following organization: Agency for Toxic Substances & Disease Registry of the United States), and then we determine the exploitation conditions so as to keep the production of hydrogen sulfide below this legal maximum content.

3. Production of the Hydrocarbons

By applying the exploitation conditions determined in step 2, for example the amount, flow rate, temperature of the steam injected, or type of material, the hydrocarbons are produced observing the legal norms and minimizing the effects on the equipment.

Computer Program Product

Moreover, the invention relates to a computer program product downloadable from a communication network and/or recorded on a computer-readable medium and/or executable by a processor, comprising program code instructions for carrying out the method as described above, when said program is executed on a computer.

Non-Limiting Example of Application

The features and advantages of the method according to the invention are illustrated in the context of the exploitation of bituminous sands of the Fisher Field (Foster Creek project) in Alberta, a province in the west of Canada, by a so-called SAGD technique (“Steam-assisted gravity drainage”).

For this example of application, the method according to the invention is applied with the following assumptions:

-   -   the compositional representation of the hydrocarbons of the SARA         type is used, considering two pseudo-constituents for the resins         (RES1, RES2) and two pseudo-constituents for the asphaltenes         (ASP1, ASP2);     -   a single solid pseudo-constituent SLD is considered;     -   it is assumed that each of the pseudo-constituents is         represented by a pseudo-molecule of the type         C_(nC)H_(nH)S_(nS)O_(nO);     -   the system of reactions (2) is used for simulating the         aquathermolysis reaction on the bituminous sands from the field         under investigation;     -   the kinetic model is established on the basis of system of         reactions (2) and the systems of equations (3), (4) and (5).

For this application of the method according to the invention, experimental measurements were performed beforehand and are presented in Table 1. Table 1 summarizes the results from elemental analyses performed in the laboratory on samples of bituminous sands from the field under investigation (Lamoureux-Var and Barroux, 2013). More precisely, this table gives the values of the ratios S/C, H/C obtained at the end of aquathermolysis (after 203 h), and O/C at the start of aquathermolysis for the pseudo-constituents SAT, ARO, RES, ASP and SLD.

Table 2 shows the number of carbon atoms adopted for the pseudo-constituents SAT, ARO, RES1, RES2, ASP1, and ASP2. This number of atoms was selected from a database of molecular weights (see Barroux et al. 2013). To simplify the equations, the numbers of carbon atoms adopted for the two pseudo-constituents describing the resins fraction were selected as equal (i.e. n_(CRES1)=n_(CRES2)).

TABLE 1 X = S X = H X = 0 Rx/c SAT 0.00000 1.91090 0.00000 Rx/c ARO 0.02172 1.38026 0.00354 Rx/c RES 0.02263 1.29116 0.03292 Rx/c ASP 0.02652 1.02020 0.01001 Rx/c SLD 0.07491 2.21299 0.00000

TABLE 2 nC_(SAT) 14 nC_(ARO) 66 nC_(RES1/2) 94 nC_(ASP1) 194 nC_(ASP2) 256

Substituting these experimental values for the variables in the equations of system (2) governing the model of the aquathermolysis reactions allows the resultant system of equations to be solved as a function of the stoichiometric coefficients of the kinetic model. This solution is performed using the formal program Maple. By construction, the stoichiometric coefficients of the first 4 reactions of system (2) depend only on the pseudo-stoichiometric coefficients of the reaction scheme for sulfur.

For the first 2 kinetic reactions (i.e. ri with i={1.2}), we get:

a _(i H2S) =f(a _(S) _(iH2S) )=2.1272a _(Si H2S)

a _(i SAT) =f(a _(S) _(iH2S) ,a _(S) _(iSLD) )=1.2385+18.9119a _(Si H2S)+20.3750a _(Si SLD)

a _(i ARO) =f(a _(S) _(iH2S) ,a _(S) _(iSLD) )=1.4839−1.4839a _(Si H2S)−1.4839a _(Si SLD)

a _(i SLD) =f(a _(S) _(iSLD) )=31.5522a _(Si SLD)

a _(i H20) =f(a _(S) _(iH2S) ,a _(S) _(iSLD) )=−(1.2385+18.9119a _(Si H2S)+20.3750a _(Si SLD))

a _(i CO2) =f(a _(S) _(iH2S) ,a _(S) _(iSLD) )=1.9931+9.6293a _(Si H2S)+10.3608a _(Si SLD),  (7a)

For reaction r3, we get:

a _(3 H2S) =f(a _(S) _(3H2S) )=5.1448a _(S3 H2S)

a _(3 SAT) =f(a _(S) _(3H2S) ,a _(S) _(3SLD) )=−3.6582+15.2560a _(S3 H2S)+10.2238a _(S3 SLD)

a _(3 ARO) =f(a _(S) _(3H2S) ,a _(S) _(3SLD) )=3.5890−15860a _(S3 H2S)−3.5890a _(S3 SLD)

a _(3 SLD) =f(a _(S3SLD))=76.3120a _(S3 SLD)

a _(3 H20) =f(a _(S) _(3H2S) ,a _(S) _(3SLD) )=−(15.5805+45.7402a _(S3 H2S)+49.2787a _(S3 SLD))

a _(3 CO2) =f(a _(S) _(3H2S) ,a _(S) _(3SLD) )=8.3419+23.2894a _(S3 H2S)+25.0586a _(S3 SLD),  (7b)

For reaction r4, we get:

a _(4 H2S) =f(a _(S) _(4H2S) )=6.7891a _(S4 H2S)

a _(4 SAT) =f(a _(S) _(4H2S) ,a _(S) _(4SLD) )=−4.8273+20.1316a _(S4 H2S)+13.4912a _(S4 SLD)

a _(4 ARO) =f(a _(S) _(4H2S) ,a _(S) _(4SLD) )=4.7360−4.7360a _(S4 H2S)−4.7360a _(S4 SLD)

a _(4 SLD) =f(a _(S) _(4SLD) )=100.7004a _(S4 SLD)

a _(4 H2O) =f(a _(S) _(4H2S) ,a _(S) _(4SLD) )=−(20.5598+60.3582a _(S4 H2S)+65.0276a _(S4 SLD))

a _(4 CO2) =f(a _(S) _(4H2S) ,a _(S) _(4SLD) )=11.0079+30.7325a _(S4 H2S)+33.0671a _(S4 SLD).  (7c)

As the saturates do not contain any sulfur, the stoichiometric coefficients associated with the last reaction (reaction r5) do not depend on the matrix of the coefficients [a_(Sij)] and are fully constrained by the atomic balance of reaction 5. We then get:

a _(5 H2O)=−7.3118

a _(5 CO2)=3.6559

a _(5 CH4)=10.3441  (7d)

The compositional kinetic model thus obtained is then coupled to the PumaFlow reservoir simulator (IFP Energies nouvelles, France) in order to carry out reservoir simulations involving aquathermolysis reactions. The same thermodynamic properties were selected for the 2 pseudo-constituents RES1 and RES2 associated with the resins fraction, i.e. MW_(RES1/2)=1320 g/mol. This assumption makes it possible to simplify the compositional kinetic model derived from equations (3), (4), and (5).

To calibrate the kinetic model, aquathermolysis experiments on a sample of oil sand from the Fisher Field in Canada (see for example Lamoureux-Var and Lorant (2005a, 2005b)) are simulated in the laboratory. In parallel, a model is set up for numerical simulation of these aquathermolysis experiments. This model (called “0D” as there is no flow) consists of a grid that models the reactor surrounded by several grids representing the furnace used in the experiments. The central grid of the reactor represents the experimental gold tube in which the aquathermolysis reactions take place. The Peng-Robinson equation of state is used for the reservoir simulations of the aquathermolysis experiments in the laboratory. The numerical results are compared with the variations by mass of the SARA fractions and H₂S observed experimentally. The results for the SARA fractions are expressed as instantaneous mass of the component per initial mass of the component (gram by gram) whereas the production of H₂S is evaluated as mass of H₂S per total initial mass of the SARA components (gram by gram). This scaling makes it possible to compare the numerical results with the experimental results, limited to reproduction of the experiment in terms of mass fraction of the different components.

Calibration of the parameters of the thermokinetic model, namely the kinetic parameters (frequency factor and activation energy) of the five reactions of system (2) and the pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined in (1), was performed by means of an inversion loop (using the CougarFlow inversion software (IFP Energies nouvelles)) directly coupled to the PumaFlow reservoir simulator (IFP Energies nouvelles), without an intermediate step. The convergence is evaluated using an objective function that calculates the differences between the normed mass predictions of the simulator and the respective experimental data for H₂S, Saturates, Aromatics, Resins and Asphaltenes. For optimal reproduction of the emissions of H₂S relative to the mass of oil, the weighting of the term for H₂S is increased relative to the other terms. The Gauss-Newton algorithm is then used for optimization of the object function. Note that if the experiments in the laboratory supply the whole of the reaction scheme for sulfur, calibration of the compositional kinetic model for reservoir simulation may be limited to calibration of the kinetic parameters (frequency factors and activation energies).

The values of the kinetic parameters (frequency factors and activation energies) and the values of the pseudo-stoichiometric coefficients obtained after calibration with the experimental data are summarized in Table 3. The associated stoichiometric coefficients, obtained using system of equations (7), for each of the reactions r1 to r5 and for each pseudo-constituent and constituent involved in system of equations (7), are presented in Table 4.

FIG. 1 presents the evolution over time T (in days) of the mass M of H₂S relative to the initial total mass of the SARA pseudo-constituents, obtained by the present invention, carried out with the parameters defined above (continuous curve), and experimental method (continuous curve in segments). FIGS. 2A, 2B, 2C, and 2D present the evolution over time T (in days) of the mass M of the pseudo-constituents SAT, ARO, RESP and ASP respectively relative to their initial mass, obtained by the present invention, carried out with the parameters defined above (continuous curves), and by the experimental method (continuous curves in segments). In contrast to the results obtained with a method based on patent application FR 3002969 (U.S. Ser. No. 14/200,682), the experimental data for the SARA pseudo-constituents are not perfectly reproduced by the kinetic model according to the invention. The reason arises from the dependences introduced between the different parameters of the calibration of the kinetic model with equations (3) to (5) defined above. Note that patent application FR 3002969 (U.S. Ser. No. 14/200,682) allows good reproduction of the results of experimental measurements, as calibration in this application does away with many theoretical constraints (atomic balances) and experimental constraints (elemental analysis), and so benefits from additional degrees of freedom relative to the present invention. Nevertheless, the present invention makes it possible to reproduce the experimental results entirely satisfactorily, while respecting the kinetic parameters and pseudo-stoichiometric coefficients determined in the calibration step, as well as the constraints imposed by the equations of atomic balances and the data from elemental analysis. The parameters presented in Table 3 and the corresponding stoichiometric coefficients, derived from equations (7) and shown in Table 4, are then used for a compositional reservoir simulation.

TABLE 3 Frequency Activation factor energy Reaction (Day⁻¹) (kJ/mol) aSH2S aSSLD r1 1.00E+19 204.30 0.369 0.000 r2 5.00E+18 222.22 0.899 0.151 r3 4.50E+18 201.34 0.651 0.349 r4 2.00E+18 216.67 0.960 0.040 r5 3.82E+18 209.09 —

TABLE 4 Reaction H₂O H₂S SAT ARO SLD CO₂ CH₄ r1 −8.22 0.78 1.90 0.94 0.00 5.55 — r2 −21.3 1.91 5.88 0.00 4.76 12.2 — r3 −62.6 3.35 9.84 0.00 26.6 32.2 — r4 −81.1 6.52 15.0 0.00 4.03 41.8 — r5 −7.31 — −1 — — 3.66 10.34

The characteristics of the reservoir model used for modeling the field under investigation are presented in Table 5. The region of the reservoir is rectangular with the respective dimensions 420, 150 and 18 meters in directions X, Y and Z. The grid used for simulation is a Cartesian grid of 3375 grid cells (1×75×25). The two horizontal wells are located at the center of the Y axis and are a distance of 6 meters apart along the Z axis. The length of the wells along the X axis is equal to the width of the reservoir, i.e. 420 meters. The reservoir simulation is performed in a vertical section perpendicular to the Y axis, characterized by permeability and homogeneous porosity. In the reservoir simulations simulating the SAGD method, the oil-gas system is described using tables of equilibrium constants.

TABLE 5 Depth of the top of the reservoir, m 300 Overall dimensions in the X, Y, Z directions, m 420, 150, 18 Permeability, horizontal, vertical, mD 10 000, 3 Porosity 0.37 Initial pressur @300 m, bar 29 Initial temperature, ° C. 17.0 Oil density, API 10 Oil viscosity, cP 3.8E+06 Initial water saturation 0.22 Initial SAT fraction, molar fraction 0.60752 Initial ARO fraction, molar fraction 0.14992 Initial RES1 fraction, molar fraction 0.04071 Initial RES2 fraction, molar fraction 0.14499 Initial ASP1 fraction, molar fraction 0.01871 Initial ASP2 fraction, molar fraction 0.03815

The initial pressure is 29 bar at the top of the reservoir, which is located at a depth of 300 meters. The initial composition of the fluid is summarized in Table 5 and is derived from experimental measurements on the field under investigation. Further details concerning characterization of the oil and the relative permeabilities used are available in (Barroux et al., 2013). Before starting steam injection, the wells are preheated for a period of 4 months to mobilize the oil in the vicinity.

FIG. 3 shows the simulated production P of H₂S as a function of time T (in days), expressed in liters of H₂S produced per m³ of oil produced at the surface, obtained by the present invention (curve designated NUM) carried out with the parameters and assumptions defined above. This figure also shows the production of H₂S observed in situ (curve designated MES). It is deduced from measurements performed between 2005 and 2012 on the field under investigation; said measurements are published by the oil companies Encana and Cenovus, on the website of the Energy Resources Conservation Board (2012). This figure shows that the present invention, carried out with the parameters and assumptions defined above, does not allow the experimental production data to be reproduced exactly. This is explained by the fact that on the one hand the reservoir model used is extremely simplified (porosity and permeability are assumed to be homogeneous and the general parameters used for modeling the Athabasca oil sand reservoir may have differences with the specific parameters of the field investigated), and on the other hand, the reservoir simulation was limited to two wells, whereas the observed production data are derived from a field that comprises tens of wells (the production data having been adjusted to the average for that obtained for a single well for the purposes of the example). Nevertheless, the results obtained by carrying out the invention are of the same order of magnitude (of the order of about a hundred) as the production data, allowing the present invention to be validated at the reservoir scale.

FIGS. 4A and 4B show the variation of the composition of oil produced in surface conditions, as a function of time. In particular, FIG. 4A presents the evolution of the molar fraction F of the pseudo-constituents ASP, ARO, RES and of the constituent H₂S over time T (in days), and FIG. 4B presents the evolution of the molar fraction F of the pseudo-constituent SAT over time T (in days). It is clear from these figures that the oil composition changes between the start of production and the end of the simulation, almost 10 years later. In particular, the amount of saturates (SAT) and aromatics (ARO) in the oil produced has increased overall, whereas the amount of resins (RES) and asphaltenes (ASP) has decreased overall, which is consistent with the experimental results previously reported in the literature concerning this field (for example Belgrave et al., 1997).

Thus, the present invention adheres more closely to the theory representing the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances of sulfur, but also of carbon, hydrogen and possibly oxygen; possibility of including water in the system of reactions), but also takes into account certain experimental measurements that are available (such as elemental analyses) in the elaboration of the reaction mechanism. For this purpose, the stoichiometric coefficients associated with the reactions are expressed in terms of molar fraction. This kinetic model also ensures consistency between the thermodynamic parameters of the constituents, their pseudo-molecular formula and the reaction scheme. 

1. A method for exploiting an underground deposit of hydrocarbons containing organosulfur compounds, characterized in that: A. an amount of hydrogen sulfide (H₂S) produced over time by a phenomenon of aquathermolysis induced by a thermal process such as steam injection in said deposit, is determined from a grid representation of said deposit, based on experimental measurements performed on at least one sample of said hydrocarbons and/or a rock sample from said deposit, employing the following steps: i. constructing an elementary reaction scheme representative of a material balance for the element sulfur based on at least one compositional representation of the hydrocarbons, said representation describing said hydrocarbons as different pseudo-constituents, at least one solid pseudo-constituent, at least one constituent H₂S, and pseudo-stoichiometric coefficients relating to said pseudo-constituents and constituents; ii. constructing a kinetic model based on at least one system of reactions simulating said phenomenon of aquathermolysis, said reaction scheme, atomic balances relating to each of said reactions of said system of reactions, said balances relating at least to the sulfur, carbon and hydrogen atoms, and said system of reactions being a function of stoichiometric coefficients at least relating to said pseudo-constituents and constituents; iii. constructing a thermodynamic model of the pseudo-constituents of said compositional representation; iv. calibrating a thermokinetic model, consisting of said kinetic model and said thermodynamic model, on the basis of said experimental measurements; v. determining said amount of hydrogen sulfide (H₂S) produced by performing a compositional reservoir simulation, by means of a compositional and reactive thermal simulator, said simulator employing said thermokinetic model, and by means of said grid representation; B. determining the conditions of exploitation of said deposit as a function of said amount of hydrogen sulfide; C. producing said hydrocarbons by applying said conditions of exploitation.
 2. The method as claimed in the preceding claim, wherein said compositional representation of the hydrocarbons is constituted of the following pseudo-constituents: saturated hydrocarbons, aromatic hydrocarbons, resins and asphaltenes.
 3. The method as claimed in one of the preceding claims, wherein said experimental measurements consist of aquathermolysis experiments simulated in the laboratory.
 4. The method as claimed in one of the preceding claims, wherein step ii) is carried out according to the following steps: a) defining a system of reactions describing said phenomenon of aquathermolysis in said deposit, said system being a function of at least said pseudo-constituents and at least the constituents H₂S and H₂O, and of said stoichiometric coefficients relating to each of said pseudo-constituents and constituents; b) defining a first system of equations establishing, for each of said reactions, atomic balances for the atomic elements H, C, S and O; c) defining a second system of equations linking said pseudo-stoichiometric coefficients of said reaction scheme to said stoichiometric coefficients of said system of reactions, the sum of said pseudo-stoichiometric coefficients of said reaction scheme being equal to 1; d) determining an expression for said stoichiometric coefficients of said system of reactions by jointly solving said systems of equations.
 5. The method as claimed in claim 4, wherein a third system of equations is defined linking the number of sulfur, carbon and oxygen atoms as a function of the number of carbon atoms for each of said pseudo-constituents and constituents.
 6. The method as claimed in claim 5, wherein said number of sulfur, carbon and oxygen atoms is linked as a function of said number of carbon atoms for each of said pseudo-constituents via ratios determined by elemental analyses performed on products of aquathermolysis simulated in the laboratory.
 7. The method as claimed in one of the preceding claims, wherein in step iii), at least kinetic parameters of said thermokinetic model are calibrated.
 8. The method as claimed in one of claims 1 to 6, wherein in step iii), kinetic parameters of said thermokinetic model and said pseudo-stoichiometric coefficients of said reaction scheme are calibrated.
 9. The method as claimed in one of the preceding claims, wherein, in addition, in step A), variation over time of the amount of each of said pseudo-constituents of said compositional representation is determined.
 10. The method as claimed in one of the preceding claims, wherein said conditions of exploitation are determined, adapting completion materials and/or gas treatment devices as a function of said amount of hydrogen sulfide.
 11. The method as claimed in one of the preceding claims, wherein said conditions of exploitation consist of modifying steam injection conditions so as to minimize said amount of hydrogen sulfide.
 12. The method as claimed in one of the preceding claims, wherein said conditions of exploitation are determined so as to keep production of hydrogen sulfide below a legal maximum content.
 13. A computer program product downloadable from a communication network and/or recorded on a computer-readable medium and/or executable by a processor, comprising program code instructions for carrying out the method as claimed in one of the preceding claims, when said program is executed on a computer. 